Answer: r = a + lambda*(b x c).
- A r = a + lambda*(b + c)
- B r = a + lambda*(b . c)
- C r = a + lambda*(b x c)
- D r = a + lambda*(b - c)
Correct answer: C. r = a + lambda*(b x c)
Explanation: A vector perpendicular to both b and c is their cross product n = b×c. The line through position vector a with direction n is r = a + λ(b×c), where λ∈ℝ. Answer: r = a + λ(b×c).
Triangle law of vector addition: placing vector b at the head of vector a, the diagonal from the start to the final head gives the resultant a + b.
Concept context
Vectors, dot product, cross product, and geometric applications